You can use SP (Social Points) to buy furniture from the Home Store. If you scroll through, you see some purple prices, use the Social Points on those. Some items cost 100s of SP, for example the Fondue Set in the Kitchen section costs 150 SP but you currently have 5 SP.
The other ways you can earn them is either add players through Facebook or Game Centre and complete social tasks, do Live Events which give you 2 SP or spend real money to buy them from the Online Store (in the UK, buying 10 SP costs £99).